Separate universe consistency relation and calibration of halo bias

The linear halo bias is the response of the dark matter halo number density to a long-wavelength fluctuation in the dark matter density. Using abundance matching between separate universe simulations which absorb the latter into a change in the background, we test the consistency relation between the change in a one-point function, the halo mass function, and a two-point function, the halo-matter cross-correlation in the long-wavelength limit. We find excellent agreement between the two at the 1%-2% level for average halo biases between 1 ≲b_{¯ 1}≲4 and no statistically significant deviations at the 4%-5% level out to b_¯1≈8 . The halo bias inferred assuming instead a universal mass function is significantly different and inaccurate at the 10% level or more. The separate universe technique provides a way of calibrating the linear halo bias efficiently for even highly biased rare halos in the Λ cold dark matter model. Observational violation of the consistency relation would indicate new physics, e.g. in the dark matter, dark energy, or primordial non-Gaussianity sectors.